LECTURE - 1 INTRODUCTION TO QUEUING SYSTEM

LECTURE - 1 INTRODUCTION TO QUEUING SYSTEM

Learning objective To introduce features of queuing system

9.1 Queue or Waiting lines Customers waiting to get service from server are represented by queue and also called waiting line. Unsatisfied customer due to long waiting time can be a potential loss to any service organization. Managing waiting lines is one of the foremost objective for service operations manager as prompt service delivery is one of the parameter to achieve competitive advantage. Various queuing models can be used to analyze waiting line but first let s understand the queuing system. Queue: A line of waiting customers who require service from servers. There can be two types of queues; Stereotypical and virtual described in Table 9.1. TABLE 9.1: TYPES OF QUEUES Stereotypical queues Virtual queues People waiting in a formal physical line Queue is not a physical line but virtually for service customers wait to get service Example: Passengers check-in for their Example: A customer placed on hold by boarding pass at check- in counter at a call center employee airport Servers: Individual workstations where customer receive service Queue is formed when Demand for service exceeds the capacity to serve Varying arrival times of customer Varying service time at server Consequences of excessive waiting time affecting service provider Loss of potential customer and hence sales Opportunity lost to a competitor Spread of bad word of mouth Examples of Queues

A customer waiting in a bank queue to get service from a bank teller in a bank A customer trying to book a ticket online A customer kept on hold over phone to talk to a call center executive A customer in a supermarket waiting in a queue to pay a bill of groceries bought 9.1.1 Costs associated with waiting lines Major challenge for any service organization is to determine the optimal number of servers which can reduce their operational cost of handling servers and waiting time of customer simultaneously. Following are the costs associated with waiting lines realized by service organization and customers. An employee in the service organization waiting for a customer can be A cost component in the form of unproductive wages Underutilization of capacity due to idle time at server A customer waiting for a server to get the service done incurs Opportunity cost of waiting in a queue Forgone alternative use of waiting time Service organizations cannot avoid waiting completely due to varying arrival and service time. If service organization installs less number of servers or low service capacity it can lead to long waiting time for the customer, which results in low service level. Whereas, the large number of servers may result in underutilization of service capacity if demand turns out to be less than the service capacity. So, the main objective of any service organization is to balance the cost of waiting in queue and cost of providing capacity. The trade-off between cost of providing capacity and cost of waiting time can be seen in Figure 9.1

FIGURE 9.1: BALANCING COST OF WAITING VERSUS PROVIDING CAPACITY To achieve optimal service level, the service organizations minimize the expected total cost of waiting time and cost of providing capacity. 9.1.2 Strategies to change the perception of waiting Due to the random arrival and service time, it is difficult to eliminate waiting completely. The service organizations can always manage waiting time in a productive manner by adopting some strategies as given below. Conceal the queue from arriving customer Example: Visitors at golden beach can see the queue only after entering the main gate Snake the waiting line Example: At airport the security check there is snake like queue to hide the true length of queue. Consider waiting customer as a resource in the service process Example: Waiting patient can be asked to fill the medical history record, which saves valuable physician time also Propose a component of self service Introduce a component of entertainment while waiting like animations, attractions

9.2 Features of Queuing Systems Any Queuing system is governed by certain features like arrival pattern of customers, customers decision to wait in the queue, type of queues, queue discipline and service process. These features are presented in Figure 9.2 and discussed below. FIGURE 9.2: FEATURES OF QUEUING SYSTEM 9.2.1 Calling population Calling populations deals with how service organizations obtain customers. It can be Homogenous or heterogeneous Finite number of people to be served or infinite number 9.2.2 Balk and renege Balk: After entering into service organization but without joining queue, realizing the queue to be long or slow moving the customer balk and get service elsewhere. Renege: After joining the queue, a customer may consider the delay to be intolerable and the customer leaves the queue before service is rendered. 9.2.3 Arrival Process with Inter Arrival Time Arrival rate is the rate at which customers arrive in service system

Generally represented by exponential distribution The exponential distribution has a continuous probability density function(pdf) as given below F(t) λe -λt t 0 where λ= Average arrival rate within a given interval of time T= time between arrivals e= base of natural logarithms Mean of exponential distance is = 1 / λ Variance of exponential distance is = 1 / λ 2 The cumulative distribution function(cdf) for exponential distribution is F(t) = 1- e λt t 0 CDF gives the probability that the time between arrivals will be t or less 9.2.4 Arrival process with number of arrivals Arrival process can be represented by number of arrivals during some time intervals Poisson distribution is used to get the probability of n arrivals during the time interval t Poisson distribution is a discrete probability function which is represented as F(n) = (λt) n e λt n=0,1,2. Where λ = Average arrival rate within a given interval of time t= Number of time periods of interest n= No of arrivals(0,1,2,..) Mean of poisson distribution is = λt Variance of poisson distribution is = λt

Poisson and Exponential Equivalence FIGURE 9.3: EQUIVALENCE OF POISSON AND EXPONENTIAL DISTRIBUTION 9.2.5 Queue Configuration Queue configuration can be defined with the following parameters. Number of queues in a service system Different arrangement of queues Position or turn of a customer waiting in a queue Effects of queue on customer behavior Different types of configurations can be seen in Table 9.2 TABLE 9.2: TYPES OF QUEUE CONFIGURATION Multiple Queues Single Queue Take a Number - Customer has option to decide which queue to join - Customer can switch to other queues (Jockeying) - Differentiated service - Customers join single sinnons (snake like) queue - Ensures First-come First-Served FCFS rule - Reneging is difficult - On arrival customer takes a number to indicate his or her place in line - No need for a formal line, customer are free to wander about till

- Division of labor is possible - Example: In banks or movie theaters there are multiple queues in front of different counters - Example: At airports Immigration check is done in a single queue his or her number is called - Example: Most of the fast food and now a days many banks give a token according to the order or as per the type of query and call when the turn comes 9.2.6 Queue discipline Policy of selecting the next customer from the queue for service 1. FCFS (First Come First Served): Fair policy where all customers are treated alike 2. Shortest processing time: Give priority to the customer require short processing time to minimize the average time a customer spends in the system 3. Priority: preemptive priority rule for emergency services where current service is interrupted to serve a newly arrived customer with higher priority 4. Round robin: Start partial service for customers who are waiting in queue. Customers face waiting time & get service alternatively. Give drinks to the waiting customers in a restaurant or share menu with them. 9.2.7 Service Process The service process and the distribution of service time depends on the following factors. Number of servers: Large number of servers provides more capacity and hence can handle more customers to reduce waiting time. In such case server may handle variety of requests and can give more time to each customer, which impacts the service time distribution.

Time taken at service counter or at server: It varies with different requirements of customers, capability of the employee at server and standardized versus customized service rendered. The service time is constant for standardized services. Whereas, the service time becomes random for customized service. Arrangement of servers: The arrangement of servers either in parallel or in series impact the service time. An assembly like structure may make the customer visit more than one server to complete the service. In such arrangement the server is specialized only for his/her task. In parallel arrangement of servers, all servers can be capable of performing all tasks and the customer can complete whole procedure at one server only. Server behavior: An employee may behave depending on the length of queue. If an employee has a long queue, he/she may speed up the service process and may compromise on the quality of service.